1、Designation: D4641 12Standard Practice forCalculation of Pore Size Distributions of Catalysts andCatalyst Carriers from Nitrogen Desorption Isotherms1This standard is issued under the fixed designation D4641; the number immediately following the designation indicates the year oforiginal adoption or,
2、 in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the calculation of pore size distri-butions for catalysts a
3、nd catalyst carriers from nitrogen des-orption isotherms. The computational procedure is particularlyuseful for determining how the pore volume is distributed incatalyst samples containing pores whose sizes range fromapproximately 1.5 to 100 nm (15 to 1000 ) in radius. It shouldbe used with caution
4、when applied to isotherms for samplescontaining pores both within this size range and pores largerthan 100 nm (1000 ) in radius. In such instances theisotherms rise steeply near P/Po= 1 and the total pore volumecannot be well defined. The calculations should be begun at apoint on the isotherm near s
5、aturation preferably in a regionnear P/Po= 0.99, establishing an upper limit on the pore sizedistribution range to be studied. Simplifications are necessaryregarding pore shape.Acylindrical pore model is assumed, andthe method treats the pores as non-intersecting, open-endedcapillaries which are ass
6、umed to function independently ofeach other during the adsorption or desorption of nitrogen.NOTE 1This practice is designed primarily for manual computationand a few simplifications have been made for this purpose. For computercomputation, the simplified expressions may be replaced by exact expres-s
7、ions.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish
8、 appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D3766 Terminology Relating to Catalysts and CatalysisD4222 Test Method for Determination of Nitrogen Adsorp-tion and Desorption Isotherms of Ca
9、talysts and CatalystCarriers by Static Volumetric Measurements3. Terminology3.1 DefinitionsConsult Terminology D3766.3.2 Symbols:P4(i) = pressure after equilibration during desorption,torr.P0(i) = liquid nitrogen vapor pressure, torr.Vde= see 12.4.10 and 12.5 in Test Method D4222.rk(i) = radius of i
10、nner core calculated from Kelvinequation, .T = boiling point of nitrogen, K.VL= liquid nitrogen molar volume at T,cm3/mole.g = liquid nitrogen surface tension at T, mN/m.T(i) = average thickness of the nitrogen film adsorbedon the pore walls, .rp(i) = radius of cylindrical pore given by rk(i)+t (i),
11、 .Q = volume correction factor defined as (rp/rk)2.DVT(i) = decrease in the amount of nitrogen adsorbedcaused by a lowering in relative pressure,mm3/g.DVf(i) = volume of liquid nitrogen desorbed from porewalls during thinning of the film, mm3/g.DVk(i) = liquid volume of the inner core in which capil
12、-lary condensation of the nitrogen occurs, mm3/g.DVp(i) = liquid volume contained in a group of poreshaving mean radius rp,mm3/g.1This practice is under the jurisdiction of ASTM Committee D32 on Catalystsand is the direct responsibility of Subcommittee D32.01 on Physical-ChemicalProperties.Current e
13、dition approved May 1, 2012. Published July 2012. Originally approvedin 1987. Last previous edition approved in 2006 as D464194(2006). DOI:10.1520/D4641-12.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of AST
14、MStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.(Dvp= cumulative pore volume, mm3/g.DSp(i ) = area of the pore walls of a cylinder havingv
15、olume DVp,m2/g.4. Summary of Practice4.1 The pore size distribution is determined by analyzingthe desorption data of the nitrogen isotherm. The nitrogenuptake is caused by the multilayer adsorption of a film ofnitrogen on the pore walls and by capillary condensation of thenitrogen in the “inner core
16、” regions of the pores. The relativepressure at which filling of the core occurs for a given pore sizeby capillary condensation is predicted from the Kelvin equa-tion (1).3During desorption, thinning of the multilayer filmadsorbed on the pore walls occurs in pores which havepreviously lost their cap
17、illary condensate. Corrections for filmthinning are determined by a procedure involving the surfacearea and radius of the film which becomes exposed asdesorption proceeds. In principle, the computational procedurecan be applied to either the adsorption branch or desorptionbranch of the nitrogen isot
18、herm. Unless the presence ofink-bottle shaped pores is suggested by an abrupt closure of thedesorption branch on the adsorption branch, the distributioncurve derived from the desorption data is preferred, and isdescribed in this procedure. The computational method isessentially the procedure develop
19、ed by Barrett, Joyner, andHalenda (2) except for the incorporation of a few simplifica-tions.NOTE 2In cases where it has been established that the adsorptionbranch of the nitrogen isotherm is to be analyzed, the procedure proposedby Cranston and Inkley (3) is recommended.5. Significance and Use5.1 P
20、ore volume distribution curves obtained from nitrogensorption isotherms provide one of the best means of character-izing the pore structure in porous catalysts, provided that thelimitations of the method are kept in mind. Used in conjunctionwith the BET treatment for surface area determination (4),t
21、hese methods provide an indispensable means for studying thestructure associated with pores usually important in catalysts.This practice is particularly useful in studying changes in aseries of closely related samples caused by treatments, such asheat, compression, or extrusion often used in catalys
22、t manu-facturing. Pore volume distribution curves can often providevaluable information during mechanistic studies dealing withcatalyst deactivation.6. Computational Procedure6.1 This procedure requires the use of a series of experi-mentally measured relative pressures P4(i)/P0(i) and thecorrespondi
23、ng quantities of nitrogen gas adsorbed Vde ex-pressed in units of cm3STP/g. The experimental data requiredin the use of this procedure can be measured by following thesteps outlined in Test Method D4222. Inspect the nitrogensorption isotherm in the region above P/Po= 0.95. If the solidcontains no po
24、res larger than 100 nm (1000 ) radius, theisotherm remains nearly horizontal over a range of P/Poapproaching unity and it is a simple matter to select a startingrelative pressure within this region, establishing an upper limiton the pore size range to be studied. If pores larger than 100 nm(1000 ) a
25、re present however, the isotherm rises rapidly nearP/PO= 1 and the total pore volume cannot be well defined.This limiting adsorption can then be identified reliably only ifthe temperature is very carefully controlled and there are no“cold spots” in the apparatus (which lead to bulk condensationof th
26、e gas and a false measure of the adsorption in thevolumetric method). Selecting the starting relative pressure forthe computational procedure is then made more difficult. Inmost cases a starting relative pressure of 0.99 will be suitable,which corresponds to an upper limit on pore size of 100 nm(100
27、0 ) in radius. If necessary, interpolate the values of Vdetodetermine the quantity of nitrogen gas adsorbed at the chosenstarting relative pressure.6.2 The procedure requires numerous arithmetical stepswhich can best be carried out with the aid of a work sheet. Anexample (4) of a form found useful i
28、n the calculations isprovided in Table 1. List in descending order the experimen-tally determined relative pressures P4(i)/P0( i) in Column 1,beginning with the value chosen as the starting relativepressure. Generally, values below a relative pressure of 0.25will not be required in the calculations.
29、 Convert the uptakevalues into a liquid volume (mm3/g) by multiplying the valueof Vdein cm3STP/g with the conversion factor 1.5468 derivedfrom VL= 34.67 cm3/mole. List in Column 9 the correspondingquantities of nitrogen adsorbed.6.3 For each relative pressure, calculate a value for theradius of the
30、core, rk, by means of the Kelvin equation,RT ln P4/P0! 522gVLrk(1)given in the formrkA! 529.574ln P4/P0!(2)with T = 77.35 K; g = 8.88 mN/m; and VL= 34.67 cm3/mole. List the values in Column 2. For each successivedecrement in relative pressure, calculate rk, the mean of thevalues of rkfor the present
31、 and previous pressures, and listthese mean values in Column 3.6.4 The average thickness, t, of the multilayer film ofnitrogen adsorbed on the walls of the pores at each relativepressure is used to calculate the amount of nitrogen desorbedfrom the film in pores which have lost their capillary conden
32、-sate. For each relative pressure, calculate a value for the filmthickness from the expression (5)t A! 5F13.990.034 2 log P4/P0!G12(3)and list the values in Column 4. For each successivedecrement in relative pressure, calculate the differences in thevalues of t, and list these differences as Dt in C
33、olumn 5.6.5 Since a cylindrical pore model is assumed, the radius ofthe pore, rp, is given by addition of the core radius, rk, and thefilm thickness value, t. Add the values in Column 2 to thecorresponding values in Column 4 and record the results in3The boldface numbers in parentheses refer to a li
34、st of references at the end ofthis standard.D4641 122Column 6 as rp. For each successive decrement in relativepressure, calculate rp, the mean of the pore radii, rp, for thepresent and previous pressures, and record these values inColumn 7.6.6 Compute the quantity (rp/rk)2from the values listed inCo
35、lumns 7 and 3. This quantity will be used later to correct thecore volume to the volume for each group of pores. The corevolume is the region within the pore that fills by capillarycondensation of the nitrogen. List the computed values inColumn 8 as the volume correction factor, Q.NOTE 3For a cylind
36、rical pore rpand rkare related to Q by the exactexpression:Q 5 rp/ rk1Dt!#2(4)For rk30,Dt 1%rk. Simplifying Q by eliminating Dt gives ( rp/rk)2.6.7 The amounts of nitrogen desorbed for each successivedecrement in relative pressure are calculated by progressivesubtraction of the values of the amounts
37、 of nitrogen adsorbed,Vde, listed in Column 9 from the succeeding one. Computethese differences and list the values in Column 10 as, DVT.Each value of DVTexcept for the initial one in line 2 containscontributions from the amounts of nitrogen given up by loss ofcapillary condensate and by thinning of
38、 the nitrogen filmadsorbed on the walls of pores which have previously releasedtheir capillary condensate. The initial value of DVTis duesolely to the amount of nitrogen contributed from loss ofcapillary condensate, since it is assumed that at the highestrelative pressure all of the pores are comple
39、tely filled withnitrogen, and that no thinning of the nitrogen film occurs forthe first decrement in relative pressure.6.8 In completing the calculation to obtain a value for thepore volume, D Vp, corresponding to each mean pore size, rp,of a group of pores, it will be necessary to work through thec
40、alculation for each line before proceeding to the next line. DVfin Column 11 is the amount of nitrogen given up duringdesorption from thinning of the nitrogen film adsorbed on porewalls. For line 2, DVfequals zero and the value of DVTisassigned to DVk, the volume of the inner core which fills bycapi
41、llary condensation of the nitrogen. Multiply the value ofDVkby the corresponding volume correction factor, Q, listed inColumn 8 to obtain D Vp. List the value in Column 13 of line2.6.9 Calculate the surface area of the pore walls contained involume DVpas follows:DSp m2/g! 5 20 3DVprp(5)Using the val
42、ue of DVpfrom Column 13 and the correspond-ing value of rpfrom Column 7, compute a value for DSpand listit in Column 14. A value for the total surface area of the poresthat have become exposed is obtained by summation of thevalue for D Spwith other DSpvalues in all preceding lines ofColumn 14. List
43、the value of total area in Column 15 as (DSp.TABLE 1 Pore Distribution Computational Work SheetSample Identification _ Date_1P4/P02rk3rk4t5Dt6rp7rp8Q9Vdemm3/g10DVTmm3/g11DVfmm3/g12DVkmm3/g13DVpmm3/g14DSpm2/g15(DSpm2/g16(DVpmm3/g xcirc Column 2: rk529.574lnP4/P0!Column 11: DVf5 0.085 Dt (DSppreceding
44、 line! Column 13: DVp5DVk3 QColumn 4: t 5F13.990.034 2 log P4/P0!G1/2Column 12: DVk5DVT2DVfColumn 14: DSp5 20 3 DVp/ rp!D4641 123A value for the cumulative pore volume is obtained bysummation of the value DVpwith other DVpvalues in allpreceding lines of Column 13. List the value of the cumulativepor
45、e volume in Column 16 as (DVp.NOTE 4The expression relating the surface area of the pore wallscontained in volume DVpis as follows:DSpm2/g! 5 2 3DVprp3 104(6)with DVpin cubic centimetres and rpin angstroms. Converting cubiccentimetres to cubic millimetres gives rise to the conversion factor of 20in
46、the preceding equation.6.10 An essential feature of this test method is that thevolume of nitrogen lost from the adsorbed multilayer film canbe calculated from the total area of the pores exposed, (DSp,and the decrease in the thickness of the film, Dt. Using thevalue (DSpfrom the preceding line, com
47、pute D Vffrom theexpressionDVf5 0.085 3Dt 3 (DSppreceding line! (7)and record the value in Column 11. Subtract the value of DVffrom DVTto obtain the value of DVkof Column 12. Multiplythe value of DVkwith the corresponding value of Q in Column8 to obtain the value of DVpof Column 13. Compute DSpand(D
48、Spfollowing the procedure in 6.9. Determine a value for(DVp.NOTE 5 See Appendix X1 for a more detailed discussion on thecalculation of values for DVfand the source of the coefficient.6.11 Repeat the calculations in 6.10 for each line down to arelative pressure lying between 0.25 and 0.30. If at anin
49、termediate relative pressure, the value of D Vkshould becomeequal to zero or negative, discontinue the calculation, and in allsubsequent calculations use the data from the preceding lineand above.NOTE 6It is generally agreed that the value of the pore size to whichthe Kelvin equation will no longer apply at the lower end of the pore sizerange varies from one adsorption system to another.As a result, difficul
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